Details

sample196.0ms

Algorithm

intervals

Results

73.0ms	34×	body	2560	valid
66.0ms	82×	body	1280	valid
20.0ms	51×	body	640	valid
9.0ms	83×	body	80	valid
6.0ms	26×	body	320	valid
4.0ms	1×	body	5120	valid
4.0ms	88×	body	80	nan
1.0ms	10×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	60	7
2	145	7
3	364	7
4	1248	7
5	5001	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 44.2b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.7b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative`

Counts

4 → 321

Calls

4 calls:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
18.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

364.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
248.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms	(pow (+ 1.0 (/ i n)) n)
351.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify70.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune784.0ms

Filtered

333 candidates to 242 candidates (72.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	324	9	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	325	9	334

Merged error: 19.4b

Counts

334 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
12.6b	(* (pow i 2) (log 1.0))
19.3b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `fma-udef`

Counts

4 → 186

Calls

4 calls:

1.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
14.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series630.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
211.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
133.0ms	(* (pow i 2) (log 1.0))
192.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify117.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	734	3209
1	3750	2968
2	5001	2968

prune687.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	189	9	198
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	190	17	207

Merged error: 8.5b

Counts

207 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b	(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
12.0b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.6b	(* (pow i 2) (log 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
9×	`times-frac`
8×	`prod-exp`
6×	`log-prod` `cbrt-unprod`
5×	`associate-r`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-r/` `associate-l/` `pow-exp` `clear-num` `log-pow` `fma-udef` `div-inv`

Counts

4 → 98

Calls

4 calls:

1.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
9.0ms	(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
3.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
6.0ms	(* (pow i 2) (log 1.0))

series606.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
226.0ms	(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
141.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
141.0ms	(* (pow i 2) (log 1.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	406	1369
1	1734	1164
2	5003	1157

prune334.0ms

Filtered

110 candidates to 74 candidates (67.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	111	16	127

Merged error: 8.5b

Counts

127 → 16

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (fma (- (* 0.5 i)) (log 1.0) (fma i 0.5 (fma (/ (log 1.0) i) n 1.0))) n)
0.1b	(* 100.0 (* (fma (- (* 0.5 i)) (log 1.0) (fma i 0.5 (fma (/ (log 1.0) i) n 1.0))) n))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
1×	`unswap-sqr`

Counts

2 → 40

Calls

2 calls:

4.0ms	(* (fma (- (* 0.5 i)) (log 1.0) (fma i 0.5 (fma (/ (log 1.0) i) n 1.0))) n)
5.0ms	(* 100.0 (* (fma (- (* 0.5 i)) (log 1.0) (fma i 0.5 (fma (/ (log 1.0) i) n 1.0))) n))

series293.0ms

Counts

2 → 6

Calls

2 calls:

137.0ms	(* (fma (- (* 0.5 i)) (log 1.0) (fma i 0.5 (fma (/ (log 1.0) i) n 1.0))) n)
155.0ms	(* 100.0 (* (fma (- (* 0.5 i)) (log 1.0) (fma i 0.5 (fma (/ (log 1.0) i) n 1.0))) n))

simplify38.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	206	609
1	767	502
2	5001	502

prune103.0ms

Filtered

46 candidates to 30 candidates (65.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	46	16	62

Merged error: 8.5b

Counts

62 → 16

regimes384.0ms

Accuracy

67.8% (5.8b remaining)

Error of 16.6b against oracle of 10.8b and baseline of 28.8b

bsearch398.0ms

Steps

Iters	Range		Point
8	1.0589020266715657e+285	5.9791226321401264e+287	3.601044061012584e+286
7	7.335847679741968e+166	1.2301374418047264e+169	8.599427634050601e+168
10	5.08584384811324e-07	57946.35045805707	0.13910335949885066
10	-7.102728357209251e-09	-9.76607821464244e-21	-7.0309412030491735e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	50
1	74	50
2	74	50

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	2935×	body	1280	valid
2.0s	928×	body	2560	valid
751.0ms	1774×	body	640	valid
229.0ms	893×	body	320	valid
191.0ms	2506×	body	80	valid
98.0ms	2274×	body	80	nan
79.0ms	469×	body	160	valid
37.0ms	8×	body	5120	valid